diff --git a/doc/_templates/autoclass.rst b/doc/_templates/autoclass.rst
new file mode 100644
index 000000000000..f974368b851b
--- /dev/null
+++ b/doc/_templates/autoclass.rst
@@ -0,0 +1,27 @@
+{{ fullname | escape | underline }}
+
+.. currentmodule:: {{ module }}
+
+.. autoclass:: {{ objname }}
+   :no-members:
+   :show-inheritance:
+
+{% if '__init__' in methods %}
+{% set caught_result = methods.remove('__init__') %}
+{% endif %}
+
+{% block methods %}
+{% if methods %}
+
+.. rubric:: Methods
+
+.. autosummary::
+   :template: autosummary.rst
+   :toctree:
+   :nosignatures:
+{% for item in methods %}
+   ~{{ name }}.{{ item }}
+{% endfor %}
+
+{% endif %}
+{% endblock %}
\ No newline at end of file
diff --git a/doc/api/index.rst b/doc/api/index.rst
index 2646cb783bcd..6f28baca0ade 100644
--- a/doc/api/index.rst
+++ b/doc/api/index.rst
@@ -57,7 +57,7 @@ Modules
    text_api.rst
    ticker_api.rst
    tight_layout_api.rst
-   transformations.rst
+   transforms_api.rst
    tri_api.rst
    type1font.rst
    units_api.rst
diff --git a/doc/api/transformations.rst b/doc/api/transformations.rst
deleted file mode 100644
index a50d35b080b8..000000000000
--- a/doc/api/transformations.rst
+++ /dev/null
@@ -1,20 +0,0 @@
-***************
-transformations
-***************
-
-.. inheritance-diagram:: matplotlib.transforms matplotlib.path
-   :parts: 1
-
-:mod:`matplotlib.transforms`
-=============================
-
-.. automodule:: matplotlib.transforms
-   :members: TransformNode, BboxBase, Bbox, TransformedBbox, Transform,
-       TransformWrapper, AffineBase, Affine2DBase, Affine2D, IdentityTransform,
-       BlendedGenericTransform, BlendedAffine2D, blended_transform_factory,
-       CompositeGenericTransform, CompositeAffine2D,
-       composite_transform_factory, BboxTransform, BboxTransformTo,
-       BboxTransformFrom, ScaledTranslation, TransformedPath, nonsingular,
-       interval_contains, interval_contains_open
-   :show-inheritance:
-
diff --git a/doc/api/transforms_api.rst b/doc/api/transforms_api.rst
new file mode 100644
index 000000000000..ee58af3403cd
--- /dev/null
+++ b/doc/api/transforms_api.rst
@@ -0,0 +1,59 @@
+**********
+transforms
+**********
+.. inheritance-diagram:: matplotlib.transforms matplotlib.path
+   :parts: 1
+
+:mod:`matplotlib.transforms`
+=============================
+
+.. currentmodule:: matplotlib.transforms
+
+.. automodule:: matplotlib.transforms
+    :no-members:
+
+Classes
+-------
+
+.. autosummary::
+    :toctree: _as_gen/
+    :template: autoclass.rst
+    :nosignatures:
+
+    TransformNode
+    BboxBase
+    Bbox
+    TransformedBbox
+    LockableBbox
+    Transform
+    TransformWrapper
+    AffineBase
+    Affine2DBase
+    Affine2D
+    IdentityTransform
+    BlendedGenericTransform
+    BlendedAffine2D
+    CompositeGenericTransform
+    CompositeAffine2D
+    BboxTransform
+    BboxTransformTo
+    BboxTransformToMaxOnly
+    BboxTransformFrom
+    ScaledTranslation
+    TransformedPath
+    TransformedPatchPath
+
+Functions
+---------
+
+.. autosummary::
+    :toctree: _as_gen/
+    :template: autosummary.rst
+    :nosignatures:
+
+    blended_transform_factory
+    composite_transform_factory
+    nonsingular
+    interval_contains
+    interval_contains_open
+    offset_copy
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 89942d87e319..e605591d1e54 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -1814,12 +1814,16 @@ def to_values(self):
     @staticmethod
     def matrix_from_values(a, b, c, d, e, f):
         """
-        (staticmethod) Create a new transformation matrix as a 3x3
-        numpy array of the form::
+        (staticmethod) Create a new transformation matrix.
 
-          a c e
-          b d f
-          0 0 1
+        Parameters
+        ----------
+        a, b, c, d, e, f: floats
+            The parameters in the transformation matrix of the form::
+
+              a c e
+              b d f
+              0 0 1
         """
         return np.array([[a, c, e], [b, d, f], [0.0, 0.0, 1.0]], float)
 
@@ -1869,13 +1873,18 @@ class Affine2D(Affine2DBase):
 
     def __init__(self, matrix=None, **kwargs):
         """
-        Initialize an Affine transform from a 3x3 numpy float array::
+        Initialize an Affine transform from a 3x3 numpy float array.
+
+        Parameters
+        ----------
+        matrix : 3 x 3 numpy float array, optional
+            The *matrix* should have the following form::
 
-          a c e
-          b d f
-          0 0 1
+              a c e
+              b d f
+              0 0 1
 
-        If *matrix* is None, initialize with the identity transform.
+            If *matrix* is None, initialize with the identity transform.
         """
         Affine2DBase.__init__(self, **kwargs)
         if matrix is None:
@@ -1893,40 +1902,48 @@ def __str__(self):
     @staticmethod
     def from_values(a, b, c, d, e, f):
         """
-        (staticmethod) Create a new Affine2D instance from the given
-        values::
+        (staticmethod) Create a new Affine2D instance.
 
-          a c e
-          b d f
-          0 0 1
+        Parameters
+        ----------
+        a, b, c, d, e, f: floats
+            The parameters in the transformation matrix of the form::
 
-        .
+              a c e
+              b d f
+              0 0 1
         """
         return Affine2D(
             np.array([a, c, e, b, d, f, 0.0, 0.0, 1.0], float).reshape((3, 3)))
 
     def get_matrix(self):
         """
-        Get the underlying transformation matrix as a 3x3 numpy array::
+        Get the underlying transformation matrix.
 
-          a c e
-          b d f
-          0 0 1
+        Returns
+        -------
+        matrix: a 3x3 numpy array
+            The form of the matrix::
 
-        .
+              a c e
+              b d f
+              0 0 1
         """
         self._invalid = 0
         return self._mtx
 
     def set_matrix(self, mtx):
         """
-        Set the underlying transformation matrix from a 3x3 numpy array::
+        Set the underlying transformation matrix.
 
-          a c e
-          b d f
-          0 0 1
+        Parameters
+        ----------
+        mtx: a 3x3 numpy array
+            The transformation matrix of the form::
 
-        .
+              a c e
+              b d f
+              0 0 1
         """
         self._mtx = mtx
         self.invalidate()